Introduction

1The Neolithic demographic transition, the spatial diffusion of agriculture in Neolithic Europe, the spatial diffusion of contraception in Victorian England, the wombling method for detecting discontinuities and barriers, the use of kriging to analyze the fertility transition in India, trend surface analysis, and autocorrelation... Jean-Pierre Bocquet-Appel has never stopped using spatial analysis to build his research in historical demography (Bocquet-Appel el al. 1996). However, spatial analysis, and more generally geography, can also clarify the mystery of urban growth and the sustainability of cities, so much questioned in the context of the ecological transition and the latest pandemic. The goal of the research sketched in this summary is to make intelligible the progressive concentration of population in these historical but universal objects, which surprisingly persistent evolutionary dynamics can be explained by their spatial interaction processes. I have sufficient affinity with demographers to present a first-person narrative chapter. The point is to describe the approach that guided the construction of a theory of the evolution of urban systems. For demographers, this approach has all the flaws and perhaps does not deserve its name because it does not respect any of the canons that demographic science has established for its scientific construction, which clearly leans towards a proper methodological individualism. However, was it necessary to wait until we had all the individual data on the behaviors and intentions of homo geographicus required to provide a geographic theory of urban evolution? In the absence of any other solution, we have provided one with the available mesoscale resources.

Meso-level geography in need of a microphone

2When I worked in the 1970s with the team led by Philippe Pinchemel on urban growth in France, I was struck by the prominence given to the urban development agents in many of the explanatory speeches: the actions of mayors, of housing builders, were often invoked as the key to the expansion of cities. However, the first statistical analyses of city growth and migration between cities (Robic and Roger-Pumain 1968) showed the widespread nature of the process. Similarly, Philippe Pinchemel, who deplored the excessive tendency of monographic research, was often irritated when the notion of a “favorable site” was promoted to explain urban success. Pinchemel ingeniously listed all the “favorable sites” devoid of any urban settlement... Thus, we were looking for less idiographic explanations and for a nomothetic construction in geography. Following the English geographer Brian Robson (1973), I was able to demonstrate the interest of simple, stochastic statistical models, such as Gibrat (1931), to describe, to a first approximation, the shape of the growth rate distribution in a system of cities (Pumain 1980, 1982a). The main interest of this model was to propose a dynamic explanation of the shape of the distribution of city sizes by indicating that this famous “Zipf’s law,” a portion of a lognormal distribution of the number of inhabitants of all the settlement units in a territory, was the result of a generalized growth process. The probability in the long term is that all the highly connected cities will have the same growth rate (relative growth, proportional to the size of the cities) but with strong spatial and temporal fluctuations.

3One of the first components of this research was creating a database that identifies and delimits coherent geographical entities, defined as multi-communal agglomerations in France (Vincent 1952), to consider the process of city expansion in both demographic and spatial dimensions. This database reconstructs urban agglomerations systematically over a long-term period, making it possible to measure growth over reasonably short time intervals. This is possible because of the frequency of population censuses in France between 1831 and 1975 (Pumain 1982a - see also Pumain and Riandey 1986; Bretagnolle 1999; Guérois and Paulus 2002 for subsequent updates). The second component of the approach is the match between the data analyzed and the model’s assumptions, which unfortunately has not always been achieved in some of the countless studies dedicated to “testing” Zipf’s law and Gibrat’s growth model (Pumain 2012b).

4Three major conclusions resulting from this initial research performed with limited statistical and computer resources have been confirmed by subsequent work. The first is that Gibrat’s model is, to a first approximation, a good descriptor of the growth process in urban systems composed of “integrated” territorial frameworks, i.e., guaranteeing strong interactions between cities over the long term. The second finding is that the observed deviations from the model indicate a historical increase in inequality between city sizes greater than predicted by the stochastic model, indicating a trend toward metropolization that we have subsequently observed in several territories (Pumain and Moriconi-Ebrard 1997; Cura el al. 2017). The third conclusion shows that the French settlement system can be described according to not one but two lognormal distributions. The one corresponding to the cities, which have been growing for a long time, is more unequal. In contrast, the hamlets and villages, which on average had their population peak around the last third of the 19th c. with low or negative growth rates since then, have a lower standard deviation of the distribution of the logarithms of their population size (fig. 1).

1. Two lognormal distributions for the French settlement system (modified from Béguin and Pumain 2017: 212).

5However, the most important result is the return to the theoretical development deviations from the model allow. The substantial similarity of the cities’ growth rates over the long term raises the question of the apparent autonomy of the growth process from individual decisions. However, substituting a purely statistical explanation, which also assumes that cities behave as independent units, for the social processes involved in city growth and, instead, demonstrate their multiple interactions, is not the way to build a theory of their evolution. The deviations from the model clearly reveal that these interactions are relevant, given that they are not entirely independent of city size.

From population growth to economic transformation

6This approach led to exploring explanations for city dynamics, not necessarily in local conditions favorable to their development or in the specific vision of some officials, but in the comparative observation of their transformations over time. The work initiated with Thérèse Saint-Julien on changes in job composition in all French cities with more than 20,000 inhabitants between 1954 and 1975 demonstrated not the unique nature of these trajectories but, rather, a surprising similarity in the evolution of socioeconomic profiles. This result suggests strong interdependencies between cities in the same territory, which “form a system” (Pumain and Saint-Julien 1978). Moreover, the modalities of change observed in this system of cities are similar to those described by self-organization physical theories, inferring an “order by fluctuations” that maintains an overall configuration of the system from the interactions between its components (Allen and Sanglier 1979). The persistence, or slow transformation, of the system structure (macro-geographical state of the urban system described by the shape of the distribution of city sizes, the main factors of the differential activities and social composition of the cities...) is associated with considerable fluctuations in its elements’ relative situation. Therefore, at the meso-geographic level, each city transitions rapidly between “stages” of demographic growth, stagnation, and decline. Alternatively, cities may experience slower changes in their rank in the size hierarchy over the medium term. Also, they may display decennial changes in their socioeconomic profile, which are sometimes leading, sometimes in step with, or lagging behind a common transformation (Pumain and Saint-Julien 1979). While some of these inflections can be interpreted as “local” singularities or bifurcations, it is only when the system becomes unstable, as a result of an external disturbance (e.g. for cities, a new wave of socioeconomic innovations) or the magnification of internal fluctuations (e.g. a persistent, differential rate of adaptation that occurs between groups of cities) that bifurcations can emerge at the macro-geographic level of the system of cities.

7Most of the fluctuations in individual city trajectories do not affect the system’s overall structure, which we characterized at the time by the principal components identified by factor analysis and combining many interrelated city descriptors. We have proposed an interpretation of these components by linking them to the diffusion process of socioeconomic innovations affecting all cities to a greater or lesser extent. However, these processes leave traces of variable length in the form of specializations more or less related to the city size, depending on the degree of selectivity and the scale of the innovation waves. Thus, we had a first dimension of the socioeconomic differentiation of cities, expressing their “brand image” in the second half of the 20th c., which reflected a reversal of the cities’ attraction since the 19th c. The working-class cities that concentrated manufacturing activities in the north and east of the country became the poorest and least attractive, while the cities growing since the 1960s were mainly located in the southern and western regions neglected by the first industrial revolution. Furthermore, we have highlighted the emergence, through the gradual magnification of small fluctuations, of another component, indicative of the selections made between cities by the innovations of the Trente Glorieuses period, which we described as “technical modernity.” This factor generated stronger growth in the main metropolises and in the most dynamic cities of the Rhône-Alpes region, where industry and the innovative tertiary sector were associated, as opposed to the cities in the interior that were losing ground. This “bifurcation,” which lasted several decades, supported a process of metropolization and generated a rather exceptional temporal autocorrelation in the growth rates of French cities, illustrating a singularity in a general dynamic of “coevolution” linked to the size of the cities and their location (Paulus 2004; fig. 2).

2. Socioeconomic coevolution of French cities 1960-2000 (modified from Paulus 2004).

8Therefore, the shifts in various singular cities’ trajectories are explained through faster growth at a given time or through a degree of specialization in particular activities. Consequently, the “singularities” that produce these individual developments are understood as resulting from dynamics common to all cities in an urban theory that is no longer structuralist but is now evolutionary (Pumain 1997).

The difficulty of direct observation of most intercity interactions

9My geographical analysis of urban growth is based on the observation of cities as urban agglomerations (defined by the continuity of constructed areas) or as urban areas (daily commuting areas according to the French definition). These territorial entities combine varying numbers of individuals and companies and a diversity of institutions, which can be described at this micro-geographic level by all sorts of distinct attributes, including intentions and strategies, which are partly similar or convergent and somewhat contradictory and conflicting. Demography and sociology are mainly focused on this level of analysis of cities at the individual level. However, the observation of cities at the mesoscale, when the selected borders make sense at this level, reveals a set of characteristics specific to each city entity: for example, a recognizable urban morphology, a specific range of activities and skills that geographers translate into the identification of “urban functions” in the system of cities (Pumain and Saint-Julien 1976), or particular “urban atmospheres” according to architects, urban planners and urban ethnologists (Péneau 2000; Augoyard 2011). Moreover, these city identity expressions (Debarbieux 2006) illustrate the persistence of interurban differences over time, far beyond the timespan of the generations and cohorts of people who have worked and lived there. Social sciences that focus more on methodological individualism are therefore interested in “place effects” likely to interfere with individuals’ behavior and trajectories and explain certain inflections.

10Nonetheless, geographers also claim an interest in examining these cities’ characteristics independently. Although individual human actions and intentions are “ultimately” responsible for the observed effects, the practical impossibility of capturing all of them justifies not seeking to identify this level of detail to develop an authentic “urban science,” contrary to a certain recent international doxy (Batty 2013). This epistemological pragmatism is essential when the research aims to explain the other “location effect” produced, on this average level of urban phenomenon spatial organization, by the observable entity on a macro-geographical scale that we call “system of cities” (Pumain 2006). The hypothesis of the genesis of this macro-geographical object from interactions between cities logically emerges from observations at this level, which observe coherent and partly predictable developments.

11The most directly available statistics for measuring interactions between cities are the migratory flows observed from population censuses, which are one of the components of urban growth. We have systematically analyzed migration flows between French cities in collaboration with INED (Pinchemel el al. 1972; Balley el al. 1974). Migration is clearly the most discriminating component in the growth disparities, even if its weight has decreased proportionally over time relative to the natural balance rate. Incidentally, we have retraced the main characteristics of the territorial migratory fields identified by Daniel Courgeau (1970) after Torsten Hägerstrand (1957). Different gravity models summarize the effect of the demographic weight of geographic entities and their distances on the volume of migration flows. The first dedicated algorithms allowed us to test and compare their explanatory power (Pumain and Poulain 1985). The deviations from the models were then indicative of contrasting population dynamics according to age structure, with the strong attractions of the most urbanized regions on the active population lasting longer than those on the population as a whole (Pumain 1986). This observation underlined the importance of urban economic functions in the differentials of attraction between cities, summarized by the concept of migration filter (Balley el al. 1974), and raised questions about the differences in the migration flow patterns, economic activity, and occupation of migrants.

12I carried out multivariate analyses of the socio-professional composition of migration flows between French urban agglomerations (Pumain 1980) and compared it with the resident population (Pumain 1976). One of the main results of this work is the strong similarity between the occupational specializations of cities and the compositions of incoming and outgoing flows (Pumain 1982b). Migration flows, at the level of precision described by the socio-professional categories, are either almost entirely determined in their composition by the socio-professional profile of the cities, or they simply replace outgoing flows with incoming flows. My demographer friends paid little attention to this result, which they considered highly inaccurate to measure the effect of migration on urban change. Since the socio-professional situations of migrants were only observed during the census, and couldn’t determine any potential individual employment changes or when they occurred. Only large-scale surveys could establish the importance of these interactions at the individual level (Courgeau 1999). However, the heuristic interest of recognizing the persistence of urban specializations and attempting to understand and model their coevolution strikes me as highly relevant when it comes to interpreting territorial changes, and no doubt also to better understand the major inflections of individual mobilities. However, I remain frustrated as a geographer to insufficiently promote the interest of mesoscale research to consolidate the epistemological status of intermediate-level socio-spatial units, as advocated now by some sociologists (Grossetti 2020).

13The very low “effectiveness” of migration on urban socioeconomic change has been confirmed many times (Baccaïni and Pumain 1998). Only 1 to 2% of all exchanged flows result in quantitative population shifts or qualitative changes in the city’s activity profiles, which only occur incrementally. From an urban theory perspective, this probably means that changes in the local population’s skills also contribute to the adaptation of cities to socioeconomic change, which is probably triggered as much by information exchange and financial investment as by human transfers. For example, subsequent research has revealed that large cities with universities send more qualified people to the rest of the country than they receive, despite evidence that jobs in these cities have shifted towards a greater concentration of skilled populations during this “metropolization” period (Pumain and Saint-Julien 1990). However, Olivier Finance’s observation of transnational corporate investment at the level of settlements in urban areas indicates that “investment stocks and flows tend to select or exclude a certain number of cities on a long-term and short-term basis.” This trend favored large cities but also specific regions, according to varying hierarchical scales across sectors. However, “cities with a less dynamic reputation have managed both to attract more investment than expected given their long-term size and to attract more recent new investment” (Finance 2016: 312).

14Today, the bulk of the knowledge about interactions between cities is still inferred from the observation of their differential changes. It was only possible to combine a range of interurban flows to highlight the multi-scale organization into strongly or loosely connected subsystems of cities in the French territory recently (Berroir el al. 2017). From a dynamic modeling perspective, it remains exceedingly difficult to obtain sufficient direct information on the city-to-city interactions to have any hope of representing them in models and simulating their consequences on the evolution of cities. Flows occurring between cities based on the interactions implemented in the models cannot represent migrants or investments; they are “second-order interactions” built from state variables describing each city, adjusted by parameters (Pumain 2008). The point is not to claim that we can dispense with micro-scale work to model the evolution of cities and systems of cities. Instead, such knowledge is essential to identify which city attributes are relevant and how to structure their connections when modeling the inter-city interactions expected to occur in the genesis and evolution of systems of cities. The results of individual-level surveys are crucial (and sometimes sorely lacking) for determining plausible orders of magnitude and estimating parameter values that characterize inter-city interactions.

From differential equation models to multi-agent models to improve exploration of the urban interaction space

15The notion of self-organization suggests no explicit political or economic purpose, either in institutional terms or interpreted according to an optimized function, to explain urban systems structuring according to an architecture that is identifiable because it is persistent. The structure is instead the involuntary product of multiple interactions between multiple agents. Everyone acts according to their individual goals and strategies, but there is no need to know each one in detail to predict (or simulate) the system’s general architecture. The dynamics of change contribute to the shaping of the system through internal and external dynamic processes. If a structure emerges and is maintained long enough to be identifiable, this structure is nonetheless the product of that evolution. From this perspective, temporary changes in the trajectory of a particular city can be interpreted as local “bifurcations,” the succession of which produces the unique trajectory of each city. The longer-term spatial and temporal correlations between these trajectories define the “bifurcations” in the structure of systems of cities that can confer a particular configuration to each system. For example, the primacy of Paris in the French system of cities has persisted over centuries since the very early and lasting organization of a highly centralized territory in this part of Europe. This organization represents a singularity that distinguishes France by a significant difference in size that is rarely observed in the urban systems of developed countries. Nonetheless, the French system of cities does not escape the “trivial” generic dynamic that builds the evolutionary interdependencies between the cities of a single system from their interactions resulting in a gradual adaptation through incremental changes in their society and activities.

16Theories of self-organization provide mathematical models to understand the compatibility of these “disordered,” random” fluctuations (this does not mean that these actions are irrational or inexplicable, but that they are impossible to describe in detail, for each element simultaneously, in the totality of the system defined at the higher level of observation) with the persistence of the system’s structure, to reconcile the fast dynamics of the micro-level and the slow dynamics of the macro level, (Pumain and Sanders 2013). These models of nonlinear differential equations represent the temporal evolution of the state variables that define the macroscopic structure of the system, the microscopic interactions being represented by mathematical functions or by parameters. The advantage of these models is to shift the usual perspective in the study of geographical object transformations.

17History and geography change their interactions in the applications of dynamic models to regions (Allen and Sanglier 1979; Weidlich and Haag 1988) or cities (Pumain et al., 1989; Lepetit and Pumain 1993; Sanders 1992). Geography is no longer the theater of operations on which history records events. History is no longer the ultimate expression of local identity, conceived as the reconstruction of the irreversible temporal process that necessarily led to the geographical object observed today, in its indivisible singularity.

18Both disciplines are mutually informative by focusing on the morphogenesis of socio-spatial structures, on the processes that generate and maintain the shape of geographic space [...]. From this standpoint, we lose the notions of uniqueness and non-reproducibility associated with historical objects, but we consider the irreversibility of their singular trajectory. Thus, we recognize that processes may be formalized, that geographic objects may have a “trivial dynamic” in a historical trend that remains irreversible” (Pumain 1998: 64).

19Despite the heuristic interest of self-organization theories and associated mathematical models, such models’ practical application in geography is difficult (Pumain el al. 1989; Sanders 1992; Pumain and Sanders 2013), mainly due to the lack of flexibility of nonlinear systems of equations to represent spatial interactions. Consequently, we quickly resorted to multi-agent simulation models that allow a detailed reconstruction of these interactions, which are supposed to generate, through their recurrent operations, the differential dynamics that characterize systems of cities. Therefore, with the help of computer scientists, we designed the series of SIMPOP1 models intended primarily to test the theoretical proposals of an evolutionary theory of cities (Pumain 1997), formulated to account for the accumulated empirical observations resulting from the statistical processing of large comparative databases on different urban systems (Pumain 2012a).

20The first of the SIMPOP models (Bura el al. 1996; Sanders el al. 1997) allowed for the representation of three different types of spatial interactions according to the urban functions studied: gravitational for commercial exchanges, delimited by borders for administrative functions, and in specialized networks for activities such as manufacturing or tourism. This model suggested that a hypothesis of interactions between cities was necessary to generate their coevolution. According to the highly characteristic “rank-size law”, the system’s hierarchy does not occur without interactions between cities. However, even with a few hundred trial-and-error simulations performed “by hand” on the parameters that were not directly observable, we could not prove that this minimum condition was also necessary.

21The second version of a SIMPOP model, developed by another computer scientist, Benoît Glisse, allowed us to identify some of the processes that generate diversity in urban systems, based on a comparison between Europe and the United States (Bretagnolle el al. 2010). An initial version of the model, adjusted to the evolution of European cities over four centuries, required significant qualitative modifications to account for the evolution of American cities over almost three centuries. The singularity of a system of cities from the “New World” was thus evidenced, or at least confirmed in its broad outlines, from the necessary transformation of the multi-agent model’s rules representing the interactions between cities. Such a transformation was possible by imposing the “pioneer front” notions in territorial colonization and reliance on the “colonial metropolis” external demand to ensure the development of the system under the dynamics revealed by the empirical data calibration. Somehow, a complex system dynamic model provided a “singularity” example in the classical geography definition, linked to the geohistory of the urban system.

22At the city level, Thomas Louail’s work (2010) has the benefit of demonstrating the possibility of simulating the emergence of singular urban spatial structures, despite similar constraining dynamic processes, at the cost of defining some rules and initial conditions to differentiate the morphologies of European and North-American cities. The European structure is radioconcentric and characterized by strong internal differences in densities and prices (according to center-periphery gradients). The American structure is more homogeneous and far more widespread, according to orthogonal patterns that reduce accessibility differentials. This difference illustrates a “bifurcation” in terms of distinct alternative trajectories compatible with the same dynamic process (Prigogine and Stengers 1979).

Modeling to test theories

23Much closer collaboration between computer scientists and geographers allowed us to take a qualitatively significant step in identifying what constitutes the specificity of a system of cities beyond the genericity of the dynamic processes implemented in models designed to be as parsimonious as possible. One of the main problems of multi-agent simulations is their validation step, given that calibration cannot readily guarantee the unicity of results, either on empirical data or on theoretical hypotheses (Banos 2013).

24Following the development of the OpenMOLE simulation platform, designed to integrate sophisticated model validation processes, including genetic algorithms and a large capacity for parallel grid computing, we were able to achieve higher confidence in the quality of parameter estimation of a generic model (SimpopLocal, prepared in Clara Schmitt’s thesis (2014) with the help of the SimProcess platform developed by Sébastien Rey-Coyrehourcq (2015). The almost complete exploration of the parameter space required some 500 million replications of the same model (Schmitt el al. 2015). Thus, the theoretical assumptions tested and hypothesized to lead to the emergence of urban systems based on interactions propagating innovations between settlement centers could be considered sufficient and necessary to reconstruct an urban hierarchy. We have developed a new procedure for rigorously exploring the behavioral space of a model, which complements our ability to dynamically distinguish between the particular and the general (Reuillon el al. 2015). Moreover, a more sophisticated model calibration of the relatively singular example of the system of cities in post-soviet space (Cottineau 2014) led to an incremental method of developing such models, based on decreasing parsimony in considering the system’s generating mechanisms and its environmental constraints. A novel conception of geographic singularity is thus suggested, identifying it at different precision levels, according to an adaptable interval assessing the degree of specificity of a regional development in a generic process, for a given level of description granularity (Cottineau el al. 2015).

25We should explain this progress, which strikes me as important, both for the validation of multi-agent models and for strengthening the reliability of their implementation in the social sciences. Based on these new validation methods, this modeling allows us to obtain results that are, if not predictive, at least capable of more strictly delimiting the universe of possible developments. The SimpopLocal model used initially to test these methods identified parsimonious key parameters to generate an urban system that could evolve according to highly plausible or “average” observations during the first major transition in the history of cities, some 3-4,000 years after the Neolithic. The key parameter for urban dynamics in this model is social innovation, which emergence is effectively endogenous to the model by scaling it to the number of interactions in the population (Schmitt 2014). This choice is confirmed in retrospect by a recent article in the journal Nature Communication, which proposes generic models and explanations of the thousand-year-old evolution of settlement systems on this principle (Shin el al. 2020). Furthermore, by deploying genetic algorithms and distributed supercomputing to explore the model’s outcome data space, we were able to demonstrate, for the first time in the HSS field, that our hypotheses for reconstructing the emergence of a system of cities were both necessary and sufficient (Schmitt el al. 2015).

26The integrated modeling work, which includes theoretical proposals, harmonized empirical data, and adapted methods, has been extended by Juste Raimbault, not only on hypothetical examples but using empirical data to calibrate the models. A first model analyzes the coevolution of a system of cities and a transport network. This model incorporates network effects by assuming that their development depends on the (gravity-like) strength of interactions between cities and performs flow feedback on city growth rates (Raimbault 2020). An additional step allows the network to evolve dynamically according to flow values, following a threshold self-reinforcement process (Raimbault 2021). This model applied to the French system of cities, and the railway network between 1850 and 2000 generally supports the idea of a strong relationship between urban growth and the development of networks that support interactions between cities while showing a wide variety of coevolutionary regimes, with varying degrees of lag between the two processes. Calibration over successive periods provides information on the network interaction and growth dynamics and reproduces typical stylized features such as the tunnel effect. A similar approach has been used to show the tight relationship between population density and road network growth in Europe by reproducing the diversity of morphological organizations of the system of cities (Raimbault 2018, 2019).

Conclusion: spatial analysis and demography to anticipate the future of cities

27For geographers, studying the spatiality of societies implies considering the planet’s organization with human requirements and assumes a clear understanding of the settlement’s interactions with their environment. Figure 3 represents a schematic of the evolution of these relationships since the emergence of cities. By definition, cities base their development on networking more distant resources than the villages of the sedentary Neolithic period. However, during the four or five millennia following the emergence of cities in agrarian economies, their development remained strongly constrained by the availability of local resources and was influenced by the climatic and seismic fluctuations of their immediate environment. Besides, conflicts between neighboring cities or invasions of more distant origin often led to destruction, sometimes permanent, at least until the 14th c. The full realization of the amplifying role of the networks developed by the cities only emerged with the demographic and economic boom that prepared the first industrial revolution, spreading urbanization and its processes -including capitalism- all over the world in just two centuries. The power of urban networks may have seemed limitless until we recognized the depletion of specific resources, particularly in energy, or their excessive consumption or degradation, increasing at a higher rate than their renewal. But the established urban networks are now much more stable and universal in their coverage of territories. The interactions that support them and that they ensure should make it possible, in a system powered by science, technology, and territorial intelligence, to facilitate the necessary information exchanges to achieve the “ecological transition” and urban sustainability that are part of the United Nations’ programs (UN Habitat 2020).

3. Diagram of the evolution of systems of cities (modified from Schmitt 2014).

28With our models, we invert a “sedimentary” perspective that conceives geography as “the last layer of history.” We no longer seek to explain a location, a “geographical entity,” by taking into account its entire history, by reconstructing its unique genesis. We no longer construct history as a path that we follow backward to find an “explanation” in the biography of a place. Initially, we have been able to hypothesize that in some features, geographic objects represent specific achievements, among a range of possible achievements, of general dynamic processes with models that concede the existence of multiple solutions to the same dynamic process. Subsequently, we could postulate theoretical hypotheses describing the interaction patterns between cities through multi-agent simulation models. These interactions are difficult to observe directly in the medium and long term but are consistent with available empirical observations of changes in urban systems of different types (Pumain el al. 2015). The construction of models that are constantly improved by adding empirical data and methodological innovations within a program whose name deliberately highlights urban geodiversity2 contributes to identifying geographical singularities in the “classical” sense at different spatial and temporal scales.

29The question of the future of cities entails answering the following question: will the interurban dynamics observed so far continue in a context of slowed or even negative demographic growth and more restricted economic growth? Our research on the role and power of interactions in the morphogenesis of systems of cities tends to predict continuity of their hierarchical organization and a progression of their inequalities that only war periods have slowed down until now. Only massive and costly political interventions in small and medium-sized cities could lead to a complete reversal of the current dynamics.

30The evolutionary theory considers “urban systems” as complex, multi-scalar, and open social adapters. While always requiring a time and space context, the dynamics of these urban systems include regularities that allow them to be partly comparable and predictable across systems and time scales. Micro-geographic level interactions, resulting from the multiple interventions of many agents, produce the “behaviors” of cities and systems of cities at meso- and macro-geographic levels due to the complex and reflexive feedbacks introduced by the agents’ activities. Nevertheless, these individuals and institutions must be informed of this urban collective dynamic’s knowledge to benefit from the collective territorial intelligence they represent and to succeed in the essential adaptations required by our time’s ecological and social tensions.